A new approach in the Rayleigh-Schroedinger perturbation theory for the ro vibrational problem

For a transition vJ↔v'J' (J'=J±1) the eigenvalues and the eigenfunctions of the two considered states can be expressed respectively in terms of one variable m (transition number), relating these two states, as E vm = Σi=0 ev(i)mi, Ψvm=i=0 φv(i)m and Ev'm=Σi=oev'(i)mi , Ψv'm=Σi=o ..., where m=[J'(J'+1)-J(J+1)]/2, and the coefficients ev(i), ...v(i), ev(i) and ...v(i) are given by analytical expressions. This new expansion in the perturbation theory permits a direct calculation of many factors in spectroscopy that are expanded in terms of m as the line intensities, the wave number of a transition, the Herman-Wallis coefficients, ... etc. The numerical application shows that the present unconventional approach in the perturbation theory provides a simple and accurate method for the calculation of the eigenvalues and the eigenfunctions for the two considered states of the molecule CO and for the calculation of the Herman-Wallis coefficients for the ground state of the molecule HCl. (Author)